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Volume 6 Issue 2
Mar.  2021
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Article Contents
Liu Qianrui, Li Junyi, Chen Mohan. Thermal transport by electrons and ions in warm dense aluminum: A combined density functional theory and deep potential study[J]. Matter and Radiation at Extremes, 2021, 6(2): 026902. doi: 10.1063/5.0030123
Citation: Liu Qianrui, Li Junyi, Chen Mohan. Thermal transport by electrons and ions in warm dense aluminum: A combined density functional theory and deep potential study[J]. Matter and Radiation at Extremes, 2021, 6(2): 026902. doi: 10.1063/5.0030123

Thermal transport by electrons and ions in warm dense aluminum: A combined density functional theory and deep potential study

doi: 10.1063/5.0030123
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  • Corresponding author: a)Author to whom correspondence should be addressed: mohanchen@pku.edu.cn
  • Received Date: 2020-09-26
  • Accepted Date: 2021-01-21
  • Available Online: 2021-03-01
  • Publish Date: 2021-03-15
  • We propose an efficient scheme that combines density functional theory (DFT) with deep potentials (DPs), to systematically study convergence issues in the computation of the electronic thermal conductivity of warm dense aluminum (2.7 g/cm3 and temperatures ranging from 0.5 eV to 5.0 eV) with respect to the number of k-points, the number of atoms, the broadening parameter, the exchange-correlation functionals, and the pseudopotentials. Furthermore, we obtain the ionic thermal conductivity using the Green–Kubo method in conjunction with DP molecular dynamics simulations, and we study size effects on the ionic thermal conductivity. This work demonstrates that the proposed method is efficient in evaluating both electronic and ionic thermal conductivities of materials.
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  • [1]
    T. Guillot, “Interiors of giant planets inside and outside the solar system,” Science 286, 72–77 (1999).10.1126/science.286.5437.72
    [2]
    N. Nettelmann, A. Becker, B. Holst et al., “Jupiter models with improved ab initio hydrogen equation of state (H-REOS.2),” Astrophys. J. 750, 52 (2012).10.1088/0004-637x/750/1/52
    [3]
    F. Wesemael, H. M. Van Horn, M. P. Savedoff et al., “Atmospheres for hot, high-gravity stars. I-Pure hydrogen models,” Astrophys. J., Suppl. Ser. 43, 159 (1980).10.1086/190668
    [4]
    J. Daligault and S. Gupta, “Electron-ion scattering in dense multi-component plasmas: Application to the outer crust of an accreting neutron star,” Astrophys. J. 703, 994–1011 (2009).10.1088/0004-637x/703/1/994
    [5]
    P. Loubeyre, R. LeToullec, D. Hausermann et al., “X-ray diffraction and equation of state of hydrogen at megabar pressures,” Nature 383, 702–704 (1996).10.1038/383702a0
    [6]
    S. T. Weir, A. C. Mitchell, and W. J. Nellis, “Metallization of fluid molecular hydrogen at 140 GPa (1.4 Mbar),” Phys. Rev. Lett. 76, 1860–1863 (1996).10.1103/physrevlett.76.1860
    [7]
    W. J. Nellis, “Dynamic compression of materials: Metallization of fluid hydrogen at high pressures,” Rep. Prog. Phys. 69, 1479–1580 (2006).10.1088/0034-4885/69/5/r05
    [8]
    R. Cauble, L. B. Da Silva, T. S. Perry et al., “Absolute measurements of the equations of state of low-Z materials in the multi-Mbar regime using laser-driven shocks,” Phys. Plasmas 4, 1857–1861 (1997).10.1063/1.872362
    [9]
    J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2, 3933–4024 (1995).10.1063/1.871025
    [10]
    P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Phys. Rev. 136, B864 (1964).10.1103/physrev.136.b864
    [11]
    W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133 (1965).10.1103/physrev.140.a1133
    [12]
    Y. A. Wang and E. A. Carter, “Orbital-free kinetic-energy density functional theory,” in Theoretical Methods in Condensed Phase Chemistry (Springer, 2002), pp. 117–184.
    [13]
    E. L. Pollock and D. M. Ceperley, “Simulation of quantum many-body systems by path-integral methods,” Phys. Rev. B 30, 2555–2568 (1984).10.1103/physrevb.30.2555
    [14]
    D. M. Ceperley and E. L. Pollock, “Path-integral computation of the low-temperature properties of liquid 4He,” Phys. Rev. Lett. 56, 351–354 (1986).10.1103/physrevlett.56.351
    [15]
    E. W. Brown, B. K. Clark, J. L. DuBois et al., “Path-integral Monte Carlo simulation of the warm dense homogeneous electron gas,” Phys. Rev. Lett. 110, 146405 (2013).10.1103/physrevlett.110.146405
    [16]
    B. Militzer and K. P. Driver, “Development of path integral Monte Carlo simulations with localized nodal surfaces for second-row elements,” Phys. Rev. Lett. 115, 176403 (2015).10.1103/physrevlett.115.176403
    [17]
    B. Holst, R. Redmer, and M. P. Desjarlais, “Thermophysical properties of warm dense hydrogen using quantum molecular dynamics simulations,” Phys. Rev. B 77, 184201 (2008).10.1103/physrevb.77.184201
    [18]
    V. Recoules and J.-P. Crocombette, “Ab initio determination of electrical and thermal conductivity of liquid aluminum,” Phys. Rev. B 72, 104202 (2005).10.1103/physrevb.72.104202
    [19]
    C. Wang and P. Zhang, “Wide range equation of state for fluid hydrogen from density functional theory,” Phys. Plasmas 20, 092703 (2013).10.1063/1.4821839
    [20]
    M. Bonitz, T. Dornheim, Z. A. Moldabekov et al., “Ab initio simulation of warm dense matter,” Phys. Plasmas 27, 042710 (2020).10.1063/1.5143225
    [21]
    W. B. Hubbard, “Thermal structure of Jupiter,” Astrophys. J. 152, 745–754 (1968).10.1086/149591
    [22]
    R. W. Siegfried and S. C. Solomon, “Mercury: Internal structure and thermal evolution,” Icarus 23, 192–205 (1974).10.1016/0019-1035(74)90005-0
    [23]
    S. Labrosse, “Thermal and magnetic evolution of the Earth’s core,” Phys. Earth Planet. Inter. 140, 127–143 (2003), part of the Special Issue: Geophysical and Geochemical Evolution of the Deep Earth.10.1016/j.pepi.2003.07.006
    [24]
    M. M. Marinak, S. W. Haan, T. R. Dittrich et al., “A comparison of three-dimensional multimode hydrodynamic instability growth on various National Ignition Facility capsule designs with HYDRA simulations,” Phys. Plasmas 5, 1125–1132 (1998).10.1063/1.872643
    [25]
    D. S. Ivanov and L. V. Zhigilei, “Combined atomistic-continuum modeling of short-pulse laser melting and disintegration of metal films,” Phys. Rev. B 68, 064114 (2003).10.1103/physrevb.68.064114
    [26]
    S. X. Hu, L. A. Collins, T. R. Boehly et al., “First-principles thermal conductivity of warm-dense deuterium plasmas for inertial confinement fusion applications,” Phys. Rev. E 89, 043105 (2014).10.1103/physreve.89.043105
    [27]
    R. Kubo, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems,” J. Phys. Soc. Jpn. 12, 570–586 (1957).10.1143/jpsj.12.570
    [28]
    D. A. Greenwood, “The Boltzmann equation in the theory of electrical conduction in metals,” Proc. Phys. Soc. 71, 585–596 (1958).10.1088/0370-1328/71/4/306
    [29]
    M. P. Desjarlais, J. D. Kress, and L. A. Collins, “Electrical conductivity for warm, dense aluminum plasmas and liquids,” Phys. Rev. E 66, 025401 (2002).10.1103/physreve.66.025401
    [30]
    D. V. Knyazev and P. R Levashov, “Ab initio calculation of transport and optical properties of aluminum: Influence of simulation parameters,” Comput. Mater. Sci. 79, 817–829 (2013).10.1016/j.commatsci.2013.04.066
    [31]
    D. V. Knyazev and P. R. Levashov, “Transport and optical properties of warm dense aluminum in the two-temperature regime: Ab initio calculation and semiempirical approximation,” Phys. Plasmas 21, 073302 (2014).10.1063/1.4891341
    [32]
    M. French, A. Becker, W. Lorenzen, N. Nettelmann, M. Bethkenhagen, J. Wicht, R. Redmer, “Ab initio simulations for material properties along the Jupiter adiabat,” Astrophys. J., Suppl. Ser. 202, 5 (2012).10.1088/0067-0049/202/1/5
    [33]
    F. Lambert, V. Recoules, A. Decoster et al., “On the transport coefficients of hydrogen in the inertial confinement fusion regime,” Phys. Plasmas 18, 056306 (2011).10.1063/1.3574902
    [34]
    V. Vlček, N. de Koker, and G. Steinle-Neumann, “Electrical and thermal conductivity of Al liquid at high pressures and temperatures from ab initio computations,” Phys. Rev. B 85, 184201 (2012).10.1103/PhysRevB.85.184201
    [35]
    C. E. Starrett, J. Clérouin, V. Recoules et al., “Average atom transport properties for pure and mixed species in the hot and warm dense matter regimes,” Phys. Plasmas 19, 102709 (2012).10.1063/1.4764937
    [36]
    S. X. Hu, B. Militzer, V. N. Goncharov et al., “Strong coupling and degeneracy effects in inertial confinement fusion implosions,” Phys. Rev. Lett. 104, 235003 (2010).10.1103/physrevlett.104.235003
    [37]
    D. Sheppard, J. D. Kress, S. Crockett et al., “Combining Kohn-Sham and orbital-free density-functional theory for Hugoniot calculations to extreme pressures,” Phys. Rev. E 90, 063314 (2014).10.1103/physreve.90.063314
    [38]
    M. Pozzo, M. P. Desjarlais, and D. Alfè, “Electrical and thermal conductivity of liquid sodium from first-principles calculations,” Phys. Rev. B 84, 054203 (2011).10.1103/physrevb.84.054203
    [39]
    M. S. Green, “Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids,” J. Chem. Phys. 22, 398–413 (1954).10.1063/1.1740082
    [40]
    D. A. McQuarrie, Statistical Mechanics (Harpercollins College Div, 1976), pp. 520–521.
    [41]
    T. Kawamura, Y. Kangawa, and K. Kakimoto, “Investigation of thermal conductivity of gan by molecular dynamics,” J. Cryst. Growth 284, 197–202 (2005).10.1016/j.jcrysgro.2005.07.018
    [42]
    F. Taherkhani and H. Rezania, “Temperature and size dependency of thermal conductivity of aluminum nanocluster,” J. Nanopart. Res. 14, 1222 (2012).10.1007/s11051-012-1222-9
    [43]
    W. K. Kim, J. H. Shim, and M. Kaviany, “Thermophysical properties of liquid UO2, ZrO2 and corium by molecular dynamics and predictive models,” J. Nucl. Mater. 491, 126–137 (2017).10.1016/j.jnucmat.2017.04.030
    [44]
    C. Carbogno, R. Ramprasad, and M. Scheffler, “Ab initio Green-Kubo approach for the thermal conductivity of solids,” Phys. Rev. Lett. 118, 175901 (2017).10.1103/physrevlett.118.175901
    [45]
    A. Marcolongo, P. Umari, and S. Baroni, “Microscopic theory and quantum simulation of atomic heat transport,” Nat. Phys. 12, 80–84 (2016).10.1038/nphys3509
    [46]
    J. Kang and L.-W. Wang, “First-principles Green-Kubo method for thermal conductivity calculations,” Phys. Rev. B 96, 020302 (2017).10.1103/physrevb.96.020302
    [47]
    M. French, “Thermal conductivity of dissociating water—An ab initio study,” New J. Phys. 21, 023007 (2019).10.1088/1367-2630/ab0613
    [48]
    A. Jain and A. J. H. McGaughey, “Thermal transport by phonons and electrons in aluminum, silver, and gold from first principles,” Phys. Rev. B 93, 081206 (2016).10.1103/physrevb.93.081206
    [49]
    Y. Chen, J. Ma, and W. Li, “Understanding the thermal conductivity and Lorenz number in tungsten from first principles,” Phys. Rev. B 99, 020305 (2019).10.1103/physrevb.99.020305
    [50]
    L. Zhang, J. Han, H. Wang et al., “End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems,” in Advances in Neural Information Processing Systems (Curran Associates Inc., 2018), pp. 4436–4446.
    [51]
    H. Wang, L. Zhang, J. Han et al., “DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics,” Comput. Phys. Commun. 228, 178–184 (2018).10.1016/j.cpc.2018.03.016
    [52]
    L. Zhang, J. Han, H. Wang et al., “Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics,” Phys. Rev. Lett. 120, 143001 (2018).10.1103/physrevlett.120.143001
    [53]
    W. Jia, H. Wang, M. Chen, D. Lu, L. Lin, R. Car, W. E, and L. Zhang, “Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning,” in Proceedings of the International Conference for High Performance Computing, Networking, Storage And Analysis, SC’20 (IEEE Press, 2020).
    [54]
    D. Lu, H. Wang, M. Chen, L. Lin, R. Car, W. E, W. Jia, and L. Zhang, “86 PFLOPS deep potential molecular dynamics simulation of 100 million atoms with ab initio accuracy,” Comput. Phys. Commun. 259, 107624 (2021).10.1016/j.cpc.2020.107624
    [55]
    L. Bonati and M. Parrinello, “Silicon liquid structure and crystal nucleation from ab initio deep metadynamics,” Phys. Rev. Lett. 121, 265701 (2018).10.1103/physrevlett.121.265701
    [56]
    F.-Z. Dai, B. Wen, Y. Sun et al., “Theoretical prediction on thermal and mechanical properties of high entropy (Zr0.2Hf0.2Ti0.2Nb0.2Ta0.2)C by deep learning potential,” J. Mater. Sci. Technol. 43, 168–174 (2020).10.1016/j.jmst.2020.01.005
    [57]
    H.-Y. Ko, L. Zhang, B. Santra et al., “Isotope effects in liquid water via deep potential molecular dynamics,” Mol. Phys. 117, 3269–3281 (2019).10.1080/00268976.2019.1652366
    [58]
    J. Xu, C. Zhang, L. Zhang, M. Chen, B. Santra, and X. Wu, “Isotope effects in molecular structures and electronic properties of liquid water via deep potential molecular dynamics based on the scan functional,” Phys. Rev. B 102, 214113 (2020).10.1103/physrevb.102.214113
    [59]
    Q. Liu, D. Lu, and M. Chen, “Structure and dynamics of warm dense aluminum: A molecular dynamics study with density functional theory and deep potential,” J. Phys.: Condens. Matter 32, 144002 (2020).10.1088/1361-648x/ab5890
    [60]
    Y. Zhang, C. Gao, Q. Liu et al., “Warm dense matter simulation via electron temperature dependent deep potential molecular dynamics,” Phys. Plasmas 27, 122704 (2020).10.1063/5.0023265
    [61]
    L. H. Thomas, “The calculation of atomic fields,” Math. Proc. Cambridge Philos. Soc. 23, 542–548 (1927).10.1017/s0305004100011683
    [62]
    E. Fermi, “Un metodo statistico per la determinazione di alcune priorieta dell’atome,” Rend. Accad. Naz. Lincei 6, 32 (1927).
    [63]
    E. Fermi, “Eine statistische methode zur bestimmung einiger eigenschaften des atoms und ihre anwendung auf die theorie des periodischen systems der elemente,” Z. Phys. 48, 73–79 (1928).10.1007/bf01351576
    [64]
    C. v. Weizsäcker, “Zur theorie der kernmassen,” Z. Phys. A: Hadrons Nucl. 96, 431–458 (1935).10.1007/BF01337700
    [65]
    L.-W. Wang and M. P. Teter, “Kinetic-energy functional of the electron density,” Phys. Rev. B 45, 013196 (1992).10.1103/physrevb.45.13196
    [66]
    N. D. Mermin, “Thermal properties of the inhomogeneous electron gas,” Phys. Rev. 137, A1441 (1965).10.1103/physrev.137.a1441
    [67]
    P. Giannozzi, O. Andreussi, T. Brumme et al., “Advanced capabilities for materials modelling with quantum ESPRESSO,” J. Phys.: Condens. Matter 29, 465901 (2017).10.1088/1361-648x/aa8f79
    [68]
    J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865 (1996).10.1103/physrevlett.77.3865
    [69]
    P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 017953 (1994).10.1103/physrevb.50.17953
    [70]
    N. A. W. Holzwarth, A. R. Tackett, and G. E. Matthews, “A projector augmented wave (PAW) code for electronic structure calculations, Part I: Atompaw for generating atom-centered functions,” Comput. Phys. Commun. 135, 329–347 (2001).10.1016/s0010-4655(00)00244-7
    [71]
    H. C. Andersen, “Molecular dynamics simulations at constant pressure and/or temperature,” J. Chem. Phys. 72, 2384–2393 (1980).10.1063/1.439486
    [72]
    M. Chen, J. Xia, C. Huang et al., “Introducing PROFESS 3.0: An advanced program for orbital-free density functional theory molecular dynamics simulations,” Comput. Phys. Commun. 190, 228–230 (2015).10.1016/j.cpc.2014.12.021
    [73]
    S. Nosé, “A unified formulation of the constant temperature molecular dynamics methods,” J. Chem. Phys. 81, 511–519 (1984).10.1063/1.447334
    [74]
    W. G. Hoover, “Canonical dynamics: Equilibrium phase-space distributions,” Phys. Rev. A 31, 1695–1697 (1985).10.1103/physreva.31.1695
    [75]
    S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” J. Comput. Phys. 117, 1–19 (1995).10.1006/jcph.1995.1039
    [76]
    B. Holst, M. French, and R. Redmer, “Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen,” Phys. Rev. B 83, 235120 (2011).10.1103/physrevb.83.235120
    [77]
    A. J. Read and R. J. Needs, “Calculation of optical matrix elements with nonlocal pseudopotentials,” Phys. Rev. B 44, 13071–13073 (1991).10.1103/physrevb.44.13071
    [78]
    F. Knider, J. Hugel, and A. V. Postnikov, “Ab initio calculation of dc resistivity in liquid Al, Na and Pb,” J. Phys.: Condens. Matter 19, 196105 (2007).10.1088/0953-8984/19/19/196105
    [79]
    M. French and R. Redmer, “Electronic transport in partially ionized water plasmas,” Phys. Plasmas 24, 092306 (2017).10.1063/1.4998753
    [80]
    D. R. Hamann, “Optimized norm-conserving Vanderbilt pseudopotentials,” Phys. Rev. B 88, 085117 (2013).10.1103/physrevb.88.085117
    [81]
    D. R. Hamann, “Erratum: Optimized norm-conserving Vanderbilt pseudopotentials [Phys. Rev. B 88, 085117 (2013)],” Phys. Rev. B 95, 239906 (2017).10.1103/physrevb.95.239906
    [82]
    A. Dal Corso, “Pseudopotentials periodic table: From H to Pu,” Comput. Mater. Sci. 95, 337–350 (2014).10.1016/j.commatsci.2014.07.043
    [83]
    N. Troullier and J. L. Martins, “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43, 1993–2006 (1991).10.1103/physrevb.43.1993
    [84]
    P. Boone, H. Babaei, and C. E. Wilmer, “Heat flux for many-body interactions: Corrections to lammps,” J. Chem. Theory Comput. 15, 5579–5587 (2019).10.1021/acs.jctc.9b00252
    [85]
    C. Huang and E. A. Carter, “Transferable local pseudopotentials for magnesium, aluminum and silicon,” Phys. Chem. Chem. Phys. 10, 7109–7120 (2008).10.1039/b810407g
    [86]
    D. Kang, S. Zhang, Y. Hou, C. Gao, C. Meng, J. Zeng, and J. Yuan, “Thermally driven fermi glass states in warm dense matter: Effects on terahertz and direct-current conductivities,” Phys. Plasmas 26, 092701 (2019).10.1063/1.5104310
    [87]
    B. B. L. Witte, P. Sperling, M. French et al., “Observations of non-linear plasmon damping in dense plasmas,” Phys. Plasmas 25, 056901 (2018).10.1063/1.5017889
    [88]
    A. McKelvey, G. E. Kemp, P. A. Sterne et al., “Thermal conductivity measurements of proton-heated warm dense aluminum,” Sci. Rep. 7, 7015 (2017).10.1038/s41598-017-07173-0
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